The Resultant on Compact Riemann Surfaces
2009 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 286, no 1, 313-358 p.Article in journal (Refereed) Published
We introduce a notion of the resultant of two meromorphic functions on a compact Riemann surface and demonstrate its usefulness in several respects. For example, we exhibit several integral formulas for the resultant, relate it to potential theory and give explicit formulas for the algebraic dependence between two meromorphic functions on a compact Riemann surface. As a particular application, the exponential transform of a quadrature domain in the complex plane is expressed in terms of the resultant of two meromorphic functions on the Schottky double of the domain.
Place, publisher, year, edition, pages
2009. Vol. 286, no 1, 313-358 p.
dirichlet boundary-problem, 2-dimensional l-problem, toeplitz matrices, differential-operators, quadrature identities, integrable structure, asymptotic-behavior, extremal solutions, domains, determinants
IdentifiersURN: urn:nbn:se:kth:diva-18099DOI: 10.1007/s00220-008-0622-2ISI: 000262411000012ScopusID: 2-s2.0-58149513449OAI: oai:DiVA.org:kth-18099DiVA: diva2:336145
QC 201005252010-08-052010-08-052012-04-14Bibliographically approved